Saturation effects on synchronous generator reactive power limits: comparison of constant reactances and precise methods

Procedure (O.P.) 7.4 requires generators to follow transmission system operator (TSO) setpoints for voltage or reactive power with strict compliance rules and zonal reactive-power market mechanisms. Under these conditions, traditional approaches based on constant saturated synchronous reactances—such as defined in IEC~60034-3 and IEEE~Std~1110—are no longer adequate, as they neglect dynamic magnetic saturation and often overestimate SG capability.

To address this gap, the paper proposes a precise, real-time methodology to compute SG reactive power limits at the high-voltage (HV) side while rigorously incorporating magnetic saturation, transformer tap position, terminal-voltage constraints, under-excitation limits

(UEL), and stator and rotor current restrictions. The method is based on the saturation model of Kundur, which dynamically adjusts the d- and q-axis reactances as a function of the instantaneous internal electromotive force (EMF). This yields a saturation-dependent capability envelope that more faithfully represents the actual behavior under high excitation or large reactive loading, conditions where fixed-reactance approximations may lead to significant overestimation of capability.

A mathematical formulation is presented for HV-side reactive power limits. The proposed method accounts for: (i) the stator current boundaries, (ii) the rotor excitation limits evaluated using both constant and saturation-dependent reactances, (iii) terminal-voltage constraints requiring recalculation of the maximum or minimum limit, (iv) transformation of the UEL boundary from the generator terminals to the HV side by means of operating-point-dependent rotor angles, and (v) the net reactive capability from the HV side, taking into account the consumption of the auxiliary services. The approach directly computes both HV and lowvoltage (LV) limits, enabling integration into plant-level automatic voltage regulators (AVRs) and TSO-level secondary voltage control schemes. A detailed case study is conducted using the 720 MW SG model from Kundur’s textbook [5], connected to a 230 kV grid. The results show that incorporating a precise dynamic saturation model substantially alters the SG V-Q capability envelope compared with the constant-reactance approximation. The most pronounced effect appears in the overexcited region, where the maximum reactive power limit is significantly reduced once saturation-dependent reactances are considered. The active-power operating point further decreases both the upper and lower reactive limits, although its influence is moderate relative to saturation effects. Transformer tap position also introduces notable asymmetry: high tap settings enhance reactive injection and absorption at elevated grid voltages but reduce capability at low voltages, whereas low tap settings diminish reactive capability at high voltages while increasing it under low-voltage conditions.

Overall, the results demonstrate that dynamic saturation modelling is essential for accurate, conservative, and operationally meaningful real-time computation of SG reactive power limits.

The proposed methodology aligns with European RfG requirements, provides more reliable saturation-aware V-Q capability envelopes, and supports stable voltage control in systems with high renewable penetration. It offers a practical and precise framework for improving AVR performance, ensuring compliance, and enhancing system security under evolving operating conditions.